Question: $B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x - 2$ and $ BC = 6x - 8$ Find $AC$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {4x - 2} = {6x - 8}$ Solve for $x$ $ -2x = -6$ $ x = 3$ Substitute $3$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 4({3}) - 2$ $ BC = 6({3}) - 8$ $ AB = 12 - 2$ $ BC = 18 - 8$ $ AB = 10$ $ BC = 10$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {10} + {10}$ $ AC = 20$